Evaluation of the fingerprint profiles of the cannabinoid-1 receptor signalling via a kinetic modelling approach

Introduction: Biased agonism (aka ligand bias) is a term that is used to describe the ability of ligands to differentially regulate multiple signalling pathways when coupled to a single receptor.  Quantification of ligand bias is critical to lead compound optimisation.  Signalling is affected by rapid ligand-mediated receptor internalisation.  Hence, the conventional use of equilibrium models is not applicable as (i) receptor numbers vary with time and (ii) some kinetic profiles show non-monotonic profiles over time.  A joint kinetic model is required to quantitatively assess the time-dependent modulation of the cannabinoid-1 (CB1) receptor by ligands and provide novel insights into the complex interplay among ligands, receptors and pathways.

Aims:

1. To develop a kinetic model that describes three signalling pathways (pERK, forskolin-induced cAMP signalling, and internalisation) coupled to the CB1 receptor.
2. To visualise fingerprint profiles of bias of the CB1 ligands.

Methods: Data were available from internalisation, cAMP and pERK pathways of the CB1 receptor under multiple concentration levels of six CB₁ligands: CP55940 (CP), WIN55212-2 (WIN), anandamide (AEA), 2-arachidonoyl glycerol (2AG), Δ⁹-tetrahydrocannabinol (THC), BAY59-3074 (BAY).  A mechanism-based stimulus response model was developed using NONMEM to describe the time course of three pathways sequentially using a PPP&D modelling framework.  Internalisation was described by a target-mediated drug disposition model with a quasi-steady state assumption.  pERK and cAMP were both described by a stimulus response model linked to the constitutive activity of the pathway.  Ligand bias was determined by (1) normalising ligand specific metrics (e.g., ligand-mediated internalisation rate constant and ligand intrinsic efficacies for cAMP and pERK pathways) to the reference ligand, and then (2) further normalising it to a reference pathway (internalisation).  This double normalisation provides the standard metric used in pharmacology to describe ligand bias. The ligand bias profiles were visualised in a radar plot.

Results: The developed model adequately described the signalling profiles of the CB1 receptor.  All model parameters were precisely estimated (<50% relative standard error).  The ligand-mediated internalisation was more than 10 fold faster than constitutive internalisation.  The constitutive internalisation rate constant was typically 0.0016min^-1(16% RSE) and ligand-mediated internalisation rate constant ranged from 0.028 to 1.11 min-¹.  For the pERK pathway, the estimated system maximal stimulation was 56 fold over baseline (24% RSE).  The estimated duration of stimulation was 3.76min (3% RSE), which was consistent with observed peak time (from 3 to 5 min).  For the cAMP pathway, the estimated system maximal inhibition was 0.76 fold over baseline (5% RSE).  From visualisation of the ligand bias profiles, two biased ligands (WIN and 2AG) were identified that displayed higher selectivity towards the cAMP pathway.

Conclusion: This is the first report of a full kinetic analysis of CB1 system under non-equilibrium conditions. The kinetic modelling approach is a natural method to handle time-varying data when traditional equilibria are not present and enables quantification of ligand bias.